Zero-dimensionality and the \(GE_ 2\) of polynomial rings

DOI10.1016/0022-4049(88)90101-6zbMath0654.20058OpenAlexW2024795639MaRDI QIDQ1108386

Douglas L. Costa

Publication date: 1988

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(88)90101-6

zbMATH Keywords

zero-dimensional ring\(GE_ 2\)-ringPierce-sheafproduct of elementary and diagonal matrices

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Generators, relations, and presentations of groups (20F05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Other matrix groups over rings (20H25)

Related Items

Linear groups over general rings. I: Generalities., Noetherian-like properties and zero-dimensionality in some extensions of rings, On the structure of \(GL_ 2\) over stable range one rings, Rosenbrock's theorem for systems over von Neumann regular rings, Elementary equivalence of Chevalley groups over fields., Homomorphisms of two-dimensional linear groups over a ring of stable range one., Chevalley groups over commutative rings. I: Elementary calculations

Cites Work

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• On the \(GE_ 2\) of graded rings
• On the \(GE_n\) of a ring
• The fundamental group of the general linear group
• Semigroup rings as Prüfer rings
• On the structure of the \(GL_ 2\) of a ring
• The Conjectures of Eisenbud and Evans
• ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS
• Modules over commutative regular rings
• The Ring of Polynomials Over a von Neumann Regular Ring
• Projective modules over some non-noetherian polynomial rings